microvascular ﬂuid exchange and the revised starling principle · spotlight review microvascular...

SPOTLIGHT REVIEW

Microvascular fluid exchange and the revisedStarling principleJ. Rodney Levick1 and C. Charles Michel2*

1Physiology, Basic Medical Sciences, St George’s Hospital Medical School, London SW17 0RE, UK; and 2Department of Bioengineering, Imperial College, Exhibition Road,London SW7 2AZ, UK

Received 30 November 2009; revised 4 February 2010; accepted 18 February 2010

Time for primary review: 53 days

Microvascular fluid exchange (flow Jv) underlies plasma/interstitial fluid (ISF) balance and oedematous swelling. The traditional form of Star-ling’s principle has to be modified in light of insights into the role of ISF pressures and the recognition of the glycocalyx as the semipermeablelayer of endothelium. Sum-of-forces evidence and direct observations show that microvascular absorption is transient in most tissues; slightfiltration prevails in the steady state, even in venules. This is due in part to the inverse relation between filtration rate and ISF plasma proteinconcentration; ISF colloid osmotic pressure (COP) rises as Jv falls. In some specialized regions (e.g. kidney, intestinal mucosa), fluid absorptionis sustained by local epithelial secretions, which flush interstitial plasma proteins into the lymphatic system. The low rate of filtration andlymph formation in most tissues can be explained by standing plasma protein gradients within the intercellular cleft of continuous capillaries(glycocalyx model) and around fenestrations. Narrow breaks in the junctional strands of the cleft create high local outward fluid velocities,which cause a disequilibrium between the subglycocalyx space COP and ISF COP. Recent experiments confirm that the effect of ISF COP onJv is much less than predicted by the conventional Starling principle, in agreement with modern models. Using a two-pore system model, wealso explore how relatively small increases in large pore numbers dramatically increase Jv during acute inflammation.- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -Keywords Starling principle † Glycocalyx † Fluid exchange- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -This article is part of the Spotlight Issue on: Microvascular Permeability

1. IntroductionThe plasma, interstitial fluid (ISF), and lymph compartments are linkedin series and, in the steady state, fluid flows continuously from onecompartment to the next. Lymph drains back into the circulationchiefly at the major veins at the base of the neck. Accidental lymphaticfistulae in the neck indicate a total post-nodal lymph flow of up to 4 L/day in humans. Later work revealed that roughly half the fluid contentof afferent lymph can be absorbed by lymph node microvessels,1,2

raising the fluid turnover estimate to �8 L/day.3 This is a considerablefluid turnover; since human plasma volume is only �3 L, the entireplasma volume (except the proteins) leaves the circulation approxi-mately once every 9 h.

Substantial fluid movements between the plasma and interstitiumaccount for the rapid swelling of acutely inflamed tissues (minutes),and for the oedematous swelling of venous thrombosis, cardiacfailure, and lymphatic failure over hours to days. Conversely, haemo-dilution following an acute haemorrhage reveals a rapid absorption ofISF into the blood stream (�0.5 L in 15–30 min). Acute fluid transfersare important medically, because plasma volume is a major

determinant of the cardiac filling pressure and thus cardiac output(Starling’s ‘law of the heart’).

The fundamental principle governing such fluid shifts was laid downby Starling4 in 1896. Starling4 showed that isotonic saline injected intothe interstitial compartment of a dog hind limb appeared in thevenous blood, which became haemodiluted; but when serum ratherthan saline was injected, the fluid was not absorbed. Starling thereforeproposed that the walls of capillaries (and post-capillary venules) aresemipermeable membranes. Consequently, fluid movement acrossthem depends on the net imbalance between the osmotic absorptionpressure of the plasma proteins [colloid osmotic pressure (COP)] andthe capillary hydraulic pressure generated by the heart beat. Starlingalso recognized that since ISF has a substantial concentration ofplasma proteins, microvascular semipermeability is imperfect; theendothelial barrier slowly ‘leaks’ plasma proteins into the interstitium.The degree of leakiness to a specific solute can be quantified byStaverman’s osmotic reflection coefficient,5 s, which ranges in valuefrom 0 to 1; unity means perfect, 100% reflection, and thus noleakage of the specified solute. For a simple membrane separatingwell-stirred solutions of a single solute at two different

* Corresponding author. Tel: +44 14818823452, Email: [email protected]

Published on behalf of the European Society of Cardiology. All rights reserved. & The Author 2010. For permissions please email: [email protected].

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concentrations, it follows from the principles of irreversible thermo-dynamics5,6 that:

JvA= Lp{DP − sDP}, (1a)

where Jv is the volume filtration rate per unit endothelial area A, DPthe difference in hydrostatic pressure, and DP the difference inosmotic pressure across the membrane.

Plasma and ISF each contain many solutes (species ‘n’). Therefore,to describe fluid movement across the intervening capillary wall,Eq. (1a) should be written as:

JvA= Lp{DP −

∑snDPn}, (1b)

where∑

snDPn represents the sum of the differences in osmoticpressure exerted across the vessel walls by all the solutes in plasmaand ISF. In Eq. (1b), DP is the difference between local capillary

blood pressure Pc (diminishing with axial distance) and ISF hydrostaticpressure Pi. In most microvascular beds, only the macromolecularsolutes are present at significantly different concentrations, and forthe small solutes, s has a value of 0.1 or less. Under these conditions,Jv can be described approximately by Eq. (1a), where sDP is thedifference between the effective osmotic pressure exerted by themacromolecules (COP) in plasma (Pp) and ISF (Pi) (Figure 1A). Thisleads to the conventional expression

JvA= Lp{(Pc − Pi) − s(Pp −Pi)}. (1c)

If s has a value close to 1.0 and both Pi and Pi are close to zero, as inthe following experimental studies, Eq. (1c) summarizes the classicobservations of Landis7 and Pappenheimer and Soto-Rivera,8 whoseinvestigations are generally regarded as having established Starling’shypothesis. By measuring the prevailing Pc by direct micropuncturein single capillaries in the frog mesentery and estimating the corre-sponding rates of filtration and absorption by a red cell tracking

Figure 1 Comparison of traditional and revised views of the endothelial semipermeable membrane and the forces acting on it. (A) Traditional viewof continuous endothelium as a semipermeable membrane. (B) The glycocalyx–cleft model identifies glycocalyx as a semipermeable layer. Its under-side is subjected to the COP of fluid high inside the intercellular cleft rather than ISF, with important functional consequences.80,82 Symbols defined inmain text. Grey shade denotes concentration of plasma protein.

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method, Landis was able to demonstrate a linear relation between Jvand Pc for a population of vessels. Using isolated perfused cat and doghind limbs, Pappenheimer and Soto-Rivera ingeniously estimated themean tissue Pc from the arterial and venous pressures and vascularresistances. They were able to vary mean Pc and demonstrated alinear correlation with rates of microvascular fluid filtration/absorp-tion, estimated from changes in limb weight. Landis9 also showed,using micropipettes inserted into human nailfold skin capillaries atheart level, that blood pressure falls along a capillary, from .45–35 mmHg at the arterial end to ≥12–15 mmHg at the venular end(depending on skin temperature10,11). This gave credence to asimple picture of fluid exchange symmetry first suggested by Star-ling.12 The picture is that since Pc exceeds Pp (25–28 mmHg inhumans) over the arterial half of the capillary bed at heart level,there is fluid filtration here; and this is balanced by absorption overthe venous half, where Pc falls below Pp. The concept was developed

by Landis and Pappenheimer13 and although they circumspectly notedthat ‘with equal or greater licence (our italics) an average limb capillaryand lymphatic can be drawn’, the caveat was largely ignored and themodel became widely reproduced as an established fact (Figure 2A,left panel). It was not, however, based on a single tissue or species,because modern methods for measuring the important interstitialterms Pi and Pi in human skin were not then available.14 Over thepast 25 years, it has become clear that the conventional modeldoes not describe fluid exchange in the real microcirculation,because (i) both Pi and Pi change when Jv changes, and (ii) the fluidimmediately downstream of the semipermeable membrane (the sub-glycocalyx fluid, see later) can have a markedly different compositionto bulk ISF.

In this short review, we first consider data bearing on the conven-tional steady-state filtration–reabsorption model, then experimentshighlighting the distinction between the linear, transient fluid exchange

Figure 2 Imbalance of the classical Starling pressures when all four terms are measured in the same tissue and species. (A) Left panel showsthe traditional filtration–reabsorption model; interstitial terms are considered negligible. Right panel shows the imbalance when all four classicStarling forces are measured in human skin and subcutis at heart level.18 Black arrows indicate net force imbalance and hence the direction andthe magnitude of fluid exchange are based on the four classic forces. Dot-dashed line (red) illustrates qualitatively the much smaller net filtrationforce predicted by the glycocalyx–cleft model. For symbols see text. (B) Sum of three classic Starling forces opposing microvascular blood pressure(Pc0 ¼ sPp 2 sPi + Pi) plotted against the lowest microvascular blood pressure in different tissues (Pc). Each point is based on measurements in thesame tissue and species except the intestine (square symbols), where Pc value from rats are plotted against values Pc0 derived from cats. Closed squareis non-absorbing intestine; open square is during water absorption from gut lumen. Pc0 is capillary pressure at which the classic net filtration forcewould be zero. If venular pressure exceeds Pc0 (i.e. lies above the line of equality), venules and venous capillaries are in a state of filtration. Datafrom many laboratories.19

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vs. pressure relation and the non-linear, steady-state relation. This isfollowed by a review of the altered perspective resulting from the rec-ognition of the glycocalyx as the semipermeable layer coating theinside of the capillary wall. For a broad overview of endothelial physi-ology, see Levick.15

2. Traditional filtration–reabsorption model vs. Starlingpressures measured in specifictissues: sum-of-forces evidenceDoubts about the validity of the filtration–absorption model surfacedquietly at first. In a study of rabbit mesenteric and omental capillaries,using the Landis red cell method to monitor fluid exchange, Zweifachand Intaglietta16 noted briefly ‘We have not to date . . . encounteredvessels that consistently showed inward filtration’ (i.e. absorption).Ten years later, Levick and Michel10 documented how human skincapillary pressure increases with distance below heart level, albeit par-tially protected by postural vasoconstriction of the pre-capillaryresistance vessels; and they pointed out that tissue fluid balancecannot be maintained by downstream reabsorption in skin morethan �10 cm below heart level, because venous capillary Pc thenexceeds Pp.

10,17 In skin capillaries above the heart, Pc does notdecrease in an analogous way, because the superficial veins collapseand Pc becomes independent of further elevation.9 The issue of down-stream force balance in human skin at heart level was addressed byBates et al.,18 who measured the interstitial terms using acutelyinserted wicks. This enabled the sum of all four Starling pressuresto be calculated. They found that due to the subatmospheric natureof Pi (22 mmHg) and the substantial magnitude of Pi (15.7 mmHg),there was no net absorptive force in the cutaneous venous capillariesor venules at heart level (DP . sDP) (Figure 2A, right panel). Areview of the literature revealed the same situation in 14 differenttissues/species, including skeletal muscle (�40% of body mass) andthe lung, the tissue with the lowest Pc (Figure 2B). It is important tonote that since the Starling pressures differ between tissues andspecies, a correct sum of forces necessitates measurement of allfour forces in the same tissue.19 The absence of a net absorptiveforce in downstream vessels in the steady state is in line with theor-etical expectations, since a large DP only develops in tissues withlarge filtration rates (see later). On the basis of today’s glycocalyx–cleft model, Pi is not the correct term to use in sum-of-forcecalculations (it should be the COP beneath the glycocalyx, Pg,see below). However, the inference, i.e. no downstream netabsorptive force in the steady state, remains valid, because absorptionwould raise extravascular P and thus reinforce the sum-of-forcesargument.

3. Absorption is observedtransiently but not in the steadystate at capillary pressures belowplasma COPThe traditional steady-state filtration–reabsorption model wastested directly by Michel and Phillips.20 They used a developmentof the Landis red cell method to measure the direction and rate

of fluid exchange in perfused single capillaries of the frog mesen-tery under two different conditions. In one set of experiments,Pc was raised or lowered abruptly and fluid exchange wasmeasured immediately after the change; no time was allowed forthe extravascular forces to change (transient state). In a secondset of experiments, Pc was maintained constant for at least 2 min(and usually longer) before measuring the filtration or absorptionrate at the same value of Pc (steady state). As in Landis’s study,7

there was a linear relation between Jv/A and Pc in the transientexperiments, with transient fluid absorption when Pc was loweredbelow sPp. In the steady state, however, a dramatically differentrelation emerged (Figure 3A). When Pc exceeded sPp, filtrationrate again increased linearly with Pc; but when Pc was lower thansPp, no absorption occurred in the steady state—contrary tothe traditional downstream reabsorption model or transient state.The observations have been confirmed in both frog and rat mesen-teric vessels21 and analogous results were obtained in a study offiltration/absorption across confluent cultured endothelium in anUssing-style chamber.22

Thus, capillaries with a low blood pressure can absorb fluid transi-ently but not in the steady state (the lungs are an importantexample)—in keeping with the sum-of-forces evidence presentedearlier. Why is this so generally the case? The reason is that anadditional principle influences the steady state besides the Starlingprinciple, namely the coupling of extravascular plasma protein con-centration (and hence Pi) to capillary filtration rate. Furthermore,in some tissues, such as the lung and subcutaneous tissue, Pi increasesnon-linearly with ISF volume following increases in Jv/A.14

4. Inverse dependence ofpericapillary COP on filtration raterestricts absorption to transientstate in most tissuesAs reviewed by Taylor and Granger,23 in the steady state, the concen-tration of ISF plasma protein, Ci (determining Pi), is not a fixed quan-tity but is inversely related to the capillary filtration rate; see theextravascular dilution curve of Figure 3B, right panel.24 This isbecause ISF is continually renewed and Ci is determined dynamicallyby the rate of solute influx, Js, relative to the rate of water influx Jv.

C i =JsJv. (2)

It has been known for over 120 years (see Cohnheim25) that raisingthe capillary filtration rate ‘dilutes’ the macromolecules of the ISFand lymph.3,26 Here, we encounter a tricky situation; Jv dependspartly on extracapillary protein concentration4 [Eq. (1a–c)]; butextracapillary protein concentration depends partly on Jv [the extra-vascular dilution curve, Eq. (2)]. By dividing the standard convec-tion–diffusion equation for macromolecular transport (Js) by Jv,Michel27 derived an expression for Ci and hence Pi in terms of Jv.This was then substituted into Eq. (1c) to predict the steady-staterelation between Jv and Pc. The resulting, somewhat complex,expression [Eq. (3)] describes a curve that fits data for fluid exchangein the lung28 and human limbs29 and conforms closely to thesteady-state results of Michel and Phillips,20 with no sustained



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reabsorption even at Pc ≪ sPp (Figure 3A):

JvA= Lp DP − s2Pp

(1 − e−Pe)(1 − s.e−Pe)

[ ], (3)

where Pe ¼ Jv(1 2 s)/pdA and pd is the diffusional permeability of thecapillary barrier to the macromolecule. Pe, the Peclet number, is theratio of the velocity at which the macromolecule is washed through byconvection (solvent drag) to its diffusive velocity within the endo-thelial barrier.

It is important to note that Eq. (3) does not predict Jv/A in termsof DP, since Jv/A is present on the right-hand side too, hiddenwithin the Peclet number. The equation can be rearranged toexpress DP as a function of Jv/A (see Appendix, end of this article)and this is how it is solved.27

The reason that Eq. (3) predicts no absorption of fluid at values ofDP less than sDP is illustrated in Figure 3B (left panel). When Pc andJv are reduced, Ci and Pi rise with time [Eq. (2)]. This progressivelyreduces the absorptive force Pp–Pi, until the system finallyreverts to slight filtration, at which point a new steady state isreached.

Figure 3 Direct observation of direction of fluid exchange in capillaries in which Pc is maintained below Pp. (A) Comparison of fluid exchangeimmediately after raising or lowering Pc (transient state) and after Pc has been held constant for several minutes (steady state). Measurementsmade on single frog mesenteric capillaries perfused in situ with a Ringer solution plus serum albumin and the macromolecule Ficoll 70(Pp ¼ 32 cmH2O). When Pc was lowered from 30 to 10–15 cmH2O, a brisk uptake of fluid into the capillary was observed (e.g. green point ontransient relation). If the vessel was now perfused with Pc held constant in this range (10–15 cmH2O), absorption attenuated and after severalminutes could no longer be detected (red point on steady-state curve).20 Insets illustrate concentration of pericapillary plasma protein (dots) followingtransient water absorption (long thin arrows) and interstitial plasma protein reflection (thick curved arrow). (B) Explanatory sketches. Left panel showshow extravascular Starling forces change with time (transient state) when Pc is lowered below Pp, until a new steady state is reached. In intact tissues(cf. superfused mesentery), the absorption phase probably lowers Pi as well as raising pericapillary Pp, further cancelling the net absorptive term. Rightpanel shows how the intersection of the Starling and extravascular dilution relations determines the steady state. The curvilinear ISF relation23,24,100

describes the effect of filtration on ISF COP Pi (red line indicates corresponding Pg), while the linear, Starling’s relation describes effect of extra-capillary COP on filtration. Note that the latter relation is plotted contrary to convention, with the independent variable Pi on the y-axis and depen-dent variable Jv on the x-axis.



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Rather than solving the Starling and extravascular dilution equationsmathematically, one can draw out the linear, transient Starling’srelation [Jv vs. Pi for a given Pc, Eq. (1c)] and the interstitial dilutioncurve [Ci and hence Pi vs. Jv, Eq. (2)] on the same graph, as inFigure 3B. The intersection point is the steady-state value. The inter-cept is always a positive Jv value, even as Pc approaches zero.19

In view of the coupling of Pi to Jv, steady-state (but not transient)absorption in venous capillaries and venules is unlikely in most tissues.As Starling himself succinctly pointed out4 ‘With diminished capillarypressure there will be an osmotic absorption of salt solution from theextravascular fluid, until this becomes richer in proteids (Figure 3B, leftpanel); and the difference between its proteid osmotic pressure andthat of the intravascular plasma is equal to the diminished capillarypressure’.

Perhaps, the most surprising finding of Michel and Phillips20 was thespeed with which a steady state of fluid exchange was established. Inother tissues, the time constant is considerably longer, being of theorder of tens of minutes for microvessels in the skeletal muscles oflarge mammals.8 This may be because differences in the architectureof the pericapillary spaces allow protein concentration gradients todevelop more rapidly in some tissues than others (see below). Inaddition, the time course may be influenced by aquaporins (water-onlyconducting pores in the endothelial cell membranes), which maycontribute significantly to Lp in skeletal muscle microvessels30–32

(see later).

5. Exceptions to the ‘no steady-stateabsorption’ rule: effect of localepithelial transportThere are physiologically important exceptions to the ‘no steady-stateabsorption’ rule. In the kidney, fluid is continuously taken up by theperitubular capillaries of the cortex and by the ascending vasa recta(AVR) of the medulla. In the intestine during water absorption, fluidis absorbed continuously by the mucosal capillaries. In lymph nodes,the capillaries continuously take up fluid from the inflowing pre-nodallymph (see earlier). How do these vessels manage to break the rule?In lymph nodes, the ISF is continuously replaced by pre-nodal lymphof low protein concentration. In the kidney and the intestine, the ISF isrenewed by an independent stream of protein-free fluid which issecreted by the neighbouring epithelia. The rapid renewal of the ISFbreaks the inverse coupling between Jv and Pi [Eq. (2)] and is oftenaccompanied by a rise in Pi. When this explanation was first pro-posed,27 it appeared to be consistent with data for the small intestineand renal cortex peritubular capillaries. In these tissues, the proteinleaking into the ISF from the plasma is flushed into the local lym-phatics by the epithelial secretions. For the renal AVR, however, thetheory was less certain, because no lymphatic drainage from themedullary ISF has yet been demonstrated (see below). It should benoted that none of the microvessels in which steady-state absorptionis maintained have the low continuous endothelium found in the skin,muscle, and connective tissue.

5.1 Intestinal mucosaAlthough 70% of the blood flow to the rat ileum supplies the mucosa,direct microvascular pressure measurements showed that Pc in thefenestrated mucosal vessels lies well below Pc in the continuous capil-laries of the parallel microcirculations of the circular and longitudinal

smooth muscle.33 In cats, the intestinal lymph flow increases and itsprotein concentration decreases as fluid is absorbed from the smallintestine lumen.34 In the non-absorbing ileum, lymph COP (PL) hada mean value of 10 mmHg, whereas during brisk fluid uptake, PL

fell to 3 mmHg. The fall in Pi must be as least as great, because intes-tinal fluid absorption increases the local ISF volume, which reducesthe fractional exclusion of serum albumin.35 The latter shouldamplify the reduction in Pi. Assuming that (i) Pc is approximatelythe same in the absorbing and non-absorbing states and (ii) similarvalues for Pc are present in cat and rat mucosal capillaries, the Starlingpressures across the capillary walls change from favouring a low levelof filtration when the gut is not absorbing fluid to a state of sustainedfluid uptake when the gut is absorbing fluid (Figure 2B).

During the absorption of digested food, this simple picture may becomplicated by osmotic gradients set up by the absorbed smallsolutes. At high rates of glucose uptake, the glucose concentrationdifference across the walls of the capillaries at the tips of intestinalvilli may rise to 70 mM. Even if the osmotic reflection to glucose atthe walls of these vessels is as low as 0.01, the effective osmotic pressureset up by this glucose gradient opposes and exceeds the Starling press-ures by 15 mmHg.36 It is suggested that since the epithelial absorptionof glucose and amino acids is confined to the outer third of the villus,fluid absorbed through epithelium here might flow through the villusinterstitium to be taken up into the extensive capillary bed of thelower two-thirds of the villi36 and into the lacteals.

5.2 Renal cortexThe peritubular capillary Starling forces have been determined in ratand dog kidneys by several workers and mean values are shown inTable 1 for hydropenic rats and for rats with ISF volumes expandedby isotonic saline.37 In hydropenic rats, the Starling pressures favourfluid uptake, due to relatively low values of Pc and Pi and relativelyhigh values of Pi and Pp. Local Pp is 20–30% higher than in systemicarterial blood, because the peritubular vessels are fed with plasmaconcentrated by glomerular filtration. Following ISF expansion byintravenous saline infusion, local Pp is reduced and Pc is increasedbut the net pressure favouring fluid uptake is maintained by a largeincrease in Pi and a further fall in Pi. Similar observations have beenmade in hydropenic and volume expanded dogs. The low concen-tration of interstitial plasma protein, and hence Pi, is maintained bythe low macromolecular permeability of the fenestrated peritubularcapillaries (salbumin ≈ 0.99) and the fast production of protein-freeISF by the tubular epithelium, which flushes the relatively smallamount of plasma protein entering the cortical ISF into the corticallymphatics.

5.3 Renal medullaFluid that is absorbed by the collecting ducts from the nascent urine iscleared continuously from the medullary ISF by absorption into theAVR. Estimates of the Starling pressures across the walls of theAVR in the inner medulla of rats indicate high values of Pp and Pi

and low values of Pc and Pi, consistent with high rates of fluiduptake (Table 1).

Until recently, the low value of Pi (implying good protein clear-ance) was puzzling for two reasons. Unlike the cortical peritubularcapillaries, the AVR have a relatively high permeability to plasmaprotein; and unlike the cortex, lymphatic drainage has never beendemonstrated convincingly in the renal medulla. In both dogs38 andrats,39 labelled plasma protein reached 85% of its steady-state



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concentration in the renal medullary ISF within 3 min of its injectioninto the circulation. Ultrastructural studies have shown that ferritin,catalase, and horseradish peroxidase can pass through the fenestraeof the AVR into the ISF.40 It was believed that pre-lymphatic channelsmight drain medullary ISF41 into the renal cortex but these have notbeen confirmed. Relatively recently, Tenstad et al.42 demonstratedthat labelled albumin is cleared from the medullary ISF directly intothe blood. To account for this, MacPhee and Michel43 suggestedthat proteins might be washed into the AVR (convective proteintransport) during fluid absorption, as follows.

If convective transport of protein from ISF into AVR is to be effec-tive, the AVR s to plasma proteins has to be significantly ,1.Measurements of salbumin in single perfused AVR have given valuesbetween 0.59 and 0.78.43,44 With s in this range, and protein-freefluid from the collecting ducts replacing the fluid passing into theAVR, calculations indicated that convective clearance into the AVR(driven by the Starling pressures, Table 1) can maintain a low ISFalbumin concentration.43,45 More detailed modelling46,47 has providedadditional support for the effectiveness of convective protein uptakein the medullary countercurrent exchange system.

Although Pc in the AVR is normally greater than the surrounding Pi,it is possible that Pi might exceed Pc if medullary ISF volume is rapidlyincreased. Because the hydraulic permeability of the fenestrated AVRis high (�100 × 1027 cm/s/cmH2O), relatively large volumes offluid carrying a low concentration of protein can be driven into theAVR by a trans-endothelial hydrostatic pressure difference of just2–3 cmH2O. Although a high Pi threatens to compress the AVR,these vessels were observed not to collapse until Pc fell more than4 cmH2O below atmospheric pressure.48 The mechanical stability ofthe AVR is probably achieved by tethering of the endothelial cellsto the basal lamina of neighbouring descending vasa recta andtubules by the fine processes described by Takahashi-Iwanaga.49

6. Low filtration force paradoxOn the basis of the three lines of evidence reviewed above (sum ofmeasured forces, direct observation of fluid exchange at low Pc, andtheoretical considerations), tissue fluid balance in the muscle, skin,lung, and many other tissues is unlikely to be achieved through a near-balance of upstream filtration and downstream reabsorption in thesteady state as traditionally supposed. The drainage of capillary filtrateby the lymphatic system is therefore the dominant factor responsiblefor interstitial volume homeostasis.50 This view, however, introduces a

new problem. As pointed out by Aukland and Reed,51 the lymph flowpredicted by Eq. (1a–c) from measurements of LpA and the fourclassic Starling forces is often an order of magnitude bigger than theobserved lymph flow. To express this paradox another way, thetrue, globally averaged net filtration force calculated from the rateof generation of lymph (�1 mmHg in many tissues) is much smallerthan (Pc 2 Pi) 2 s(Pp 2 Pi), which is typically 5–10 mmHg(Figure 2B)—a discrepancy too large to dismiss as measurement error.

Several possible solutions have been proposed. In tissues withmarked arteriolar vasomotion cycles (e.g. some skeletal muscles),the arteriolar contraction phase will lower Pc in the downstream capil-lary module,8 leading to transient fluid absorption (Figure 3, transientline), followed by reversion to filtration during the arteriolar relax-ation phase, as first suggested by Chambers and Zweifach52 and devel-oped by Intaglietta and Endrich.53 In this model, fluid balance istemporal rather than spatial. Not all tissues, however, show theregular, strong vasomotion pattern on which the temporal model isbased.

More recently, exciting new insights into the complex pore struc-ture of endothelium have helped to resolve the low filtration forceparadox, by showing that the true net filtration force across endo-thelium depends not so much on Pi as on the COP of fluid justbelow the endothelial glycocalyx. In the next section, we will seethat the plasma protein concentration here can be substantially lessthan that in the bulk ISF.

7. Pore exit microgradientsand the glycocalyx–cleft modelfor continuous capillaries

7.1 Fenestrated capillariesThe classic Starling principle is symmetrical—the effect of increases inPi is predicted to have the same effects on fluid exchange asdecreases in Pp. This proved not to be the case, however, whentested in the fenestrated capillaries of synovium, the tissue that linesjoint cavities. Synovial capillaries lie just a few micrometres belowthe highly porous surface of the tissue, with small clusters of fenestrae(1–2% of surface) orientated towards the joint cavity. Consequently,intra-articular infusions of albumin can be used to alter Pi, whilemeasuring the resulting change in trans-synovial flow.54 When theresponse was compared with that brought about by changes in Pp

following intravascular albumin perfusion, a marked asymmetry was

Table 1 Starling pressures (mmHg) across the walls of peritubular capillaries and AVR in rat kidney

Cortical peritubular capillaries (salbumin ¼ 0.99)

Fluid balance Pp Pi Pc Pi sDP 2 DP

Hydropenia (mean+ SEM) 24.8+1.39 3.9+0.6 13.2+1.3 3.3+0.6 10.0

Volume expanded (mean+ SEM) 16.6+1.34 1.3+0.18 19.5+2.71 11.5+0.78 7.1

Ascending vasa recta of the renal medulla (salbumin ¼ 0.7)

Hydropenia Pp Pi Pc Pi sDP 2 DP

Papilla tip (mean+ SEM) 26.0+2.3 3.7+0.26 7.8+0.4 6.0+0.3 13.8

Papilla base (mean+ SEM) 16.7+1.3 3.7+0.26 6.7+0.48 6.0+0.3 8.4

The column headed sDP 2 DP lists values for the net Starling pressure favouring fluid absorption into the vessels. Data for cortical peritubular capillaries are based on four studiessummarized by Ulfendahl and Wolgast.37 Data for ascending vasa recta of the renal medulla are from several laboratories reviewed by MacPhee and Michel43 and Michel.45



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observed. Changes in bulk Pi had approximately one-third as mucheffect on fluid exchange as changes in Pp. A two-dimensionalmodel of synovial fluid exchange indicated that the explanation layin the development of gradients of ISF albumin concentration (andhence Pi) around the exits from the fenestral clusters, supportedby the poorly stirred nature of ISF.55 The ISF COP adjacent to thefenestrations was substantially lower than in the bulk ISF, becausethe ultrafiltrate emerging from the fenestrations diluted the immedi-ately adjacent ISF over several micrometres. In other words, plasmaultrafiltration set up ‘microgradients’ of ISF protein concentration(steep gradients over micrometre distances). The generality of thesefindings has yet to be tested in other fenestrated capillary beds.

7.2 Continuous capillaries7.2.1 Structure of intercellular pathwayAsymmetrical behaviour is even more extreme in continuous capil-laries. Here, the principal fluid-conducting pathways are through theendothelial intercellular clefts. (In most microvessels, aquaporins inthe endothelial cell membranes contribute ,10% of the hydraulicconductance, except in blood–brain barrier and possibly skeletalmuscle capillaries.56 Aquaporins have a role when interstitial osmolar-ity increases, e.g. renal descending vasa recta57 and swelling, ‘pumped’exercised muscle.30) Ultrastructural studies show that the pathwaythrough the intercellular cleft follows a long, narrow, tortuousroute.58 –60 The cumulative perimeters of the cells over 1 cm2 endo-thelium (i.e. total length of the luminal entrance to the intercellularclefts in the surface plane) is a remarkable 12–20 m. Within theclefts, however, 90% of this length is sealed by the junctionalstrands (‘tight junctions’). Fluid is funnelled through breaks in thestrands that occur at 2–4 mm intervals, each break being only 200–400 nm in length (Figure 4A). The clefts are 14–21 nm wide through-out; they do not narrow at the breaks in the junctional strands. Con-sequently, the breaks are too wide to filter out the plasma proteins(molecular diameter of serum albumin 7.1 nm). The protein-reflectingelement or ‘small pore’ system has an effective diameter of�8 nm.23,61–63 Based partly on these considerations, Curry andMichel64 proposed that the ultrafiltering pores are located in the‘fibre-matrix’ of the endothelial luminal glycocalyx, which overliesthe entrance to the clefts.

The glycocalyx is a complex, quasi-periodic network of glycosami-noglycan chains (syndecan-1, glypican, and hyaluronan) and sialoglyco-proteins, extending 60–570 nm from the endothelial luminalmembrane and coating the inner surface of capillaries, including theentrance to the intercellular cleft and most fenestrations.65– 68 Evi-dence that the glycocalyx is a major determinate of capillary per-meability includes large increases in Lp when glycocalyx-bindingproteins are removed from the capillary perfusate (the ‘protein’effect69– 72) or when glycocalyx components are removed by enzy-matic digestion,73,74 and direct observations.75 Enzyme digestionstudies also indicate that the glycocalyx mediates shear-inducedchanges in Lpd.

76 In addition to the glycocalyx–intercellular cleftpathway for water and small solutes, a separate, parallel ‘large poresystem’ transports plasma proteins slowly into the interstitial com-partment. This system comprises, controversially, large (≥50 nmwide) pores and/or vesicular transport.77– 79

7.2.2 COP difference across the intercellular pathwayMichel80 and Weinbaum81 independently recognized that sincethe pathway for macromolecules for continuous endothelium lies in

parallel with the main fluid-conducting pathway (intercellular clefts),the COP difference across the vascular barrier could no longer be cal-culated as Pp minus Pi. The COP difference that determines fluidexchange is that across the semipermeable glycocalyx. The fluid atthe abluminal side of the glycocalyx is separated from the pericapillaryISF by the tortuous path through the intercellular clefts (Figure 4A) andsince there can be protein concentration gradients along this path,Eq. (1c) should be written as:

JvA= Lp{(Pc − Pi) − s(Pp −Pg)}, (4)

where Pg is the COP of the ultrafiltrate on the underside of the gly-cocalyx. Pg can be very low, for two reasons; s is high, and theoutward flow of the ultrafiltrate prevents protein diffusion equilibriumbetween the subglycocalyx fluid and the pericapillary ISF. The diffusiondisequilibrium is greatly exacerbated by cleft structure. As the ultrafil-trate converges to pass through the narrow breaks in the intercellularjunctional strands, the fluid velocity increases at least 10-fold(Figure 4A), impeding the upstream diffusion of ISF plasma pro-teins.60,80– 82 Rough calculations indicate that even the low fluid fil-tration rate generated by a pressure difference of 1 cmH2O sufficesto prevent protein diffusion equilibrium between the subglycocalyxfluid and pericapillary ISF at the cleft exit.80,81

The above concept was developed into a two-dimensional math-ematical model by Weinbaum and coworkers.60,82 The model predictsintercellular cleft flow and plasma protein concentration in the subgly-cocalyx space for a given bulk ISF composition. Depending on the mag-nitude of the filtration pressure Pc, the model predicts big differencesbetween subglycocalyx plasma protein concentration (hence Pg) andbulk ISF protein concentration (hencePi); the ‘race’ between upstreamdiffusion and downstream washout, particularly at the junctional breaks,can result in a subglycocalyx protein concentration that is �10% of Ci

(Figure 4A). Under these circumstances, Pg is so low that the effectiveosmotic pressure difference opposing fluid filtration approximates toPp rather than the classical Starling term Pp 2 Pi (Figure 2B). Thisreduces basal Jv to similar levels as reported lymph drainage rates,and thus helps explain the low filtration force paradox.

7.2.3 Experimental tests of two-dimensional glycocalyx–cleft modelThe Weinbaum model predicts that changes in Pi around a filteringcapillary should have much less effect on Jv than predicted by theclassic Starling principle [Eq. (1c)]. The conflicting predictions weretested by Curry, Adamson and coworkers60,83 with dramatic results(Figure 4B). When interstitial albumin concentration around rapidlyfiltering frog mesenteric capillaries was raised by superfusion toequal that perfused through the capillary lumen (Pp 2 Pi ¼ 0),there was almost no change in the filtration rate—a finding incompa-tible with the classic Starling principle but in line with the Weinbaummodel.83 In a definitive study on rat mesenteric venules,60 the increasein Jv caused by raising Pi from zero to plasma level was �20% of thatpredicted by the classic Starling principle. Measurements of filtrationacross confluent cultured endothelium in a Ussing-style chamberhave likewise supported the glycocalyx–cleft model.22

7.2.4 Simplified one-dimensional model, time constants,and aquaporinsTo facilitate computation and examine events during microvascularfluid uptake, Weinbaum and coworkers84 developed a simplified



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Figure 4 The two-dimensional glycocalyx–cleft model of capillary fluid exchange, and an experimental test of its predictions. (A) A mathematicalmodel of the glycocalyx and intercellular cleft (top left).82 The semipermeable glycocalyx layer is modelled as a set of fine rods. Graph shows calcu-lated gradient of plasma protein from interstitium to the ‘protected’ subglycocalyx space, in a continuous capillary when Pc . Pp. The subglycocalyxspace is protected from equilibration with the bulk ISF by the convergent stream of ultrafiltrate passing through the narrow orifice formed by breaks inthe intercellular junctional strands. (B) Fluid exchange in single rat mesenteric venules at controlled microvascular pressure, measured by the modifiedLandis red cell method (transient state).60 The lumen was perfused with albumin solution and the exterior was superfused with saline (‘no tissuealbumin’, open symbols; Pp 2 Pi ¼ Pp) or the same albumin solution as in the lumen (‘tissue albumin’, filled symbols; Pp 2 Pi ¼ 0). Shortdashes show the expected increase in filtration rate for the latter according to the classic Starling principle. The much smaller observed responsewas as predicted by the glycocalyx–cleft model. Steady-state results (data not shown) approximated to Eq. (3).



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one-dimensional model, arguing that this more readily handles thedifferences in scale between the gradients inside the intercellularcleft and in the surrounding tissues. The one-dimensional model hasbeen used to examine the transition from non-steady-state absorp-tion to a low level of filtration. Zhang et al.21 have argued that cuffsof pericytes encircling microvessels accelerate the transition fromtransient to steady-state fluid exchange by forming ‘trapped microdo-mains’ of fluid outside the vessels. They suggest that this phenomenonaccounts for the rapid development of the steady state reported byMichel and Phillips20 and confirmed in their own laboratory.21 It ispossible that trapped microdomains are not restricted to spacesbeneath pericytes. Different tissues have different cellular architec-tures surrounding the microvessels, and this could contribute to thewide differences in the time constants of transition from transientto steady state.

The time constants could also be lengthened considerably if theaquaporin pathway contributes substantially to the microvascular Lp.Although Michel and Curry56 concluded that aquaporins represent≤10% of the Lp of most microvessels, Watson and Wolf30 –32 haveargued that their contribution to Lp may be 40–50% in cat skeletalmuscle capillaries. The osmotic pressures driving water through theaquaporin pathway are those of the capillary plasma and mean ISF. Ifaquaporins were responsible for 50% of Lp, once fluid absorption hasstarted following a fall in Pc, it should continue until the reduction inISF volume has concentrated the ISF proteins sufficiently for the conse-quent rise in Pi to reduce DP below DP. This could take an hour ormore, as calculated using typical values for capillary Lp and ISF volumein skeletal muscle. Before regarding this as an explanation of the slowdevelopment of steady-state fluid exchange in skeletal muscle, a

second consequence of a large aquaporin component of Lp should beconsidered. Since the osmotic pressure difference across the aquaporinpathway is Pp minus the mean ISF Pi (not Pg), relatively high rates offluid filtration should occur when Pc lies within its usual range(Figure 2A, right panel). One would therefore expect a brisk productionof lymph in resting skeletal muscle—whereas resting lymph flow in skel-etal muscle is so low that it is usually necessary to massage or passivelyexercise the muscle to obtain samples. Further investigation of the con-tribution of aquaporins and vasomotion to fluid exchange in skeletalmuscle is required to resolve this question.

8. Clinical importance: increasedendothelial permeability and tissueswellingMicrovascular fluid exchange underlies several major pathophysiologi-cal states. Starling himself was familiar with the transient absorption ofISF and attendant haemodilution following an acute hypotensiveepisode. Around 0.5 L of ISF can be absorbed into the human circula-tion within 15–30 min, supporting the cardiac output during hypoten-sive stress. Conversely, excessive microvascular filtration leads tointerstitial oedema—a potentially fatal condition when it affects thelungs. Oedema can result from abnormal Starling’s forces, increasedendothelial permeability (e.g. inflammation), or impaired lymphaticdrainage.50 The biochemical processes mediating increases in endo-thelial permeability were reviewed recently by Mehta and Malik.85

Here, we consider the impact of relatively small changes in endothelialmembrane properties on fluid exchange.

Figure 5 Steady-state fluid exchange simulated for a post-capillary venule, with the fluid-conducting pathways modelled as parallel small pore andlarge pore populations; effect of inflammation. (A) Basal low permeability state; 95% of the hydraulic conductance is represented by the small pores(radius ¼ 4 nm; blue curve) and 5% by large pores (radius ¼ 22.5 nm; red curve). The black solid curve shows the total fluid exchange (sum of red andblue lines) at varying values of Pc (see Appendix, end of this article). The vessel is perfused with a Ringer solution containing serum albumin(Pp ¼ 25 cmH2O). Pi is assumed to be constant and aquaporin pathway negligible (≤10% of total conductance). B. Steady-state fluid exchangewhen permeability has been increased in the same vessel. The red curve represents flow through the large pore system after inflammation hasincreased the number of large pores 10-fold. The small pore population is unchanged. The dashed lines are extrapolations of the linear parts ofthe steady-state summed relations to the pressure axis, where their intersection gives the value of the effective COP opposing fluid filtration(reduced in inflammation). Vertical arrows show typical values of microvascular pressure under basal conditions (A) and in mild inflammation (B).The rise in pressure contributes importantly to the dramatic 17-fold increase in filtration rate.



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Substantial pathology can result from relatively small reductions invascular barrier properties. Rippe and Haraldsson86 pointed out thatEq. (3) describes fluid exchange through a homoporous membrane(one where all the fluid-conducting channels have the same hydrau-lic resistance and molecular-sieving properties); whereas endo-thelium has at least two fluid-conducting pathways, the ‘smallpore’ and the ‘large pore’ pathways, as well as an aquaporinpathway in continuous capillaries. In normal healthy vessels, thesmall pores are estimated to contribute at least 95% and the largepores no more than 5% to the Lp of capillaries in skeletalmuscle.63,87 Using these values and Eq. (3), we have constructedcurves for steady-state fluid exchange (Figure 5A); see Appendix.For models that also incorporate the low-conductance aquaporinpathway, see Wolf31 and Rippe et al.88 We have assumed that thesmall pore radius is 4 nm and the large pore radius is 22.5 nm.Since the large pores contribute only 5% to the LP, this is equivalentto 19000 small pores for every large pore. In Figure 5A, we haveplotted the separate relations between Jv/A and DP for the smalland large pore systems, and the summated effect. Increased per-meability can be thought of most simply as an increase in thenumber of large pores. Figure 5B shows the effect of a 10-foldincrease in the number of large pores, with no change in the smallpore population. The resulting increase in permeability resemblesthat seen during mild inflammation.89 The increase in overall LP isjust over 50% and the overall s to serum albumin falls only from0.93 to 0.66. If the mean microvascular pressure were unchangedat just above 20 cmH2O, the addition of nine large pores per19 000 small pores would increase the fluid filtration rate fivetimes. There would also be a noticeable increase in ISF protein con-centration. The effect of this increase on Jv is greatly magnified by arise in Pc, which results from the increased blood flow and vasodila-tation of inflammation. If Pc rose to 40 cmH2O (a relative modestincrease), the net filtration of fluid into the tissue would increase17-fold (arrow, Figure 5B). Very much larger increases in LP andreductions in s occur during the first phase of acute inflam-mation.90–92 Changes of this magnitude are usually short-lived,however.

9. Advances in interstitialand lymphatic physiologySpace confines us to merely sketching advances in understanding theregulation of Pi and lymphatics. During acute inflammation Pi may fallinitially, independently of microvascular exchange, and so amplify theinitial rate of local oedema formation.93 It is suggested that connectivetissues are held under mild compression by collagen fibrils that are b1-

-integrin bonded to fibroblasts and oppose the inherent tendency ofinterstitium to expand (glycosaminoglycan swelling). Fibril detachmentserves to reduce Pi to more subatmospheric values. Supportingevidence includes a fall in Pi following treatment of the tissues withb1-integrin antibodies.

The active role of lymphatics in clearing fluid away from peripheraltissues has been supported by investigations ranging from ion channelelectrophysiology to human arm studies,94,95 and lymphatic pumpfailure has been demonstrated in human breast cancer-related lym-phoedema.96 Advances in understanding the molecular and geneticcontrol of lymphangiogenesis have underpinned insights into thedefects that underlie some hereditary lymphoedemas.97,98

10. Summary and future directionsThe COPs influencing filtration across both fenestrated and continu-ous capillaries are exerted across the endothelial glycocalyx; theosmotic pressure of the ISF does not directly determine transen-dothelial fluid exchange. There is substantial evidence that withimportant exceptions such as the renal cortex and medulla, down-stream microvessels are not in a state of sustained fluid absorptionas traditionally depicted. Although doggedly persistent in textbooksand teaching, the traditional view of filtration–reabsorption balancehas little justification in the microcirculation of most tissues. Tissuefluid balance thus depends critically on lymphatic function in mosttissues. In making these forceful statements, we are mindfulof William Harvey’s remark in his classic, De Motu Cordis (1628):‘I tremble lest I have mankind for my enemies, so much has wontand custom become second nature. Doctrine once sown strikesdeep its root, and respect for antiquity influences all men’.99

We would emphasize that despite the above advances, muchremain unknown. The time course of fluid absorption into the circu-lation requires more detailed investigation in a wider range of tissues;and the corresponding microstructure of the transendothelialpathway needs to be better defined, including estimates of the aqua-porin contribution to the overall microvascular LP, which appears tovary considerably.32 The structure and composition of the glycocalyxover fenestrations and intercellular clefts should be explored. Under-standing the regulation of the glycocalyx synthesis and turnover couldlead to novel therapeutic strategies to reduce pathologically increasedpermeability. It also worth emphasizing that little is known of thenature of fenestral diaphragms; and that the classical problem of thetransport of macromolecules through endothelia (large pores orvesicles) remains unresolved 50 years after it first became a contro-versy. Genetic knock-out mice offer a promising approach to someof these problems.79,98

AcknowledgementsWe apologize to the many authors who have contributed importantlyto this field and whose work has not been cited due to spacelimitations.

Conflict of interest: none declared.

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Appendix: two-pore model used togenerate Figure 5

The method was that described by Rippe and Haraldssson,63,87 wherethe capillary wall is modelled as an impermeable membrane of thicknessDx penetrated by two sets of cylindrical pores—small pores ofradii 4 nm and large pores of radii 22.5 nm. Lp was chosen to be

2 × 1027 cm s21 H2O21 (typical of a rat mesenteric venule), 95% of

which was accounted for by small pores and 5% by large pores. Thus,for the small pores Lp(S) ¼ 1.9 × 1027 cm s21 cmH2O

21 and for thelarge pores Lp(L) ¼ 0.1 × 1027 cm s21 cmH2O

21 and the overall hydraulicconductance is

Lp(overall) = Lp(S) + Lp(L) (A1)

Pore theory (e.g. Curry100) defines the Lp of a population of pores of con-stant radius (r) in terms of Poiseuille’s law, i.e.

Lp = pr4NDx8h

(A2)

where N is the number of pores per unit area of membrane and h isthe fluid viscosity within the pores. Thus, by assigning values for Lp(S)

and Lp(L) and pore radii, we have determined the values of NS/Dxand NL/Dx, the ratios of the numbers of small and large pores totheir length.

The partition coefficient, l, and the reflection coefficient, s, for eachset of pores to a particular solute depend on the ratio of the molecularradius (a) to the pore radius. They have been calculated from the follow-ing expressions:

l = 1 − ar

( )2(A3)

and

s = (1 − l)2 (A4)

Finally, the diffusional permeability, p, of the solute for each set of pores isrelated to the diffusion coefficient of the solute in aqueous solution, D,and a function dependent on (a/r):

p = pr2NDx

lDf (a/r) (A5)

where

far

( )= 1 − 2.1

ar

( )+ 2.09

ar

( )3−0.95

ar

( )5· · · (A6)

Equations (A1)–(A6) were used to estimate the values for Lp, s and p forserum albumin at each population of pores, assuming that a ¼ 3.6 nm foralbumin. Equation (3) was re-arranged as

DP = JV/ALp

+ s2Pp(1 − e−Pe)

(1 − s · e−Pe) (A7)

with the relevant values of Lp, s, and p, equation (A7) was used todetermine the values of DP for a range of values of JV/A for thesmall pores and the large pores. The values of JV/A at the same DPfor the small pores and the large pores were added to give theoverall JV/A for unit area of vessel wall (Figure 5A). The exercise wasrepeated for Figure 5B. Here, the contribution of Lp(S) remained con-stant at 1.9 × 1027 cm s21 H2O

21 and Lp(L) was increased 10-fold,raising the overall Lp only modestly, from 2.0 to (1.9 + 1.0) ¼ 2.9 ×1027 cm s21 H2O

21.



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